The first example I worked on is immediately below. It is a little clumsy by hand (never mind). How do I do that with Animation Nodes?
(Words below are from my little niece, when she always asks me to swing her.)
I did something a little different in the latter below. At the start of video, I gave the letters little more distance to the right. How do I swing in letters individually with Animation Nodes? Assistance appreciated. Thanks in advance.
Each character follow the path of a quarter of a circle, it starts from its right side and ends at its top. So it is clear that our characters' path should be parameterized by the equation of a circle where the parameter (angle) range between zero and $\frac{\pi}{2}$ representing the right and top of the circle respectively. The equation of a unit circle whose top is tangent to the x axis is described by the parametric equation:
$$ \begin{aligned} x &= \cos (t)\\ y &= \sin(t) - 1 \end{aligned} $$
Notice that the minus one is just to move the circle down such that its top become tangent to the x axis (Because we want the characters to end up at the x axis). We now have the location of each character. The orientation of the character along the z axis is just $-(\frac{\pi}{2}-t)=-\frac{\pi}{2}+t$. As for the scale, it just animates from zero to one. It should be noted that we can scale the circle to make the characters take a longer path. And of course, we are going to offset each character by some amount by adding to its x location. From all of this, our implementation becomes:
And to get the second result, one just modulate the parameter using a delay falloff:
